Question: Simplify the following expression and state the condition under which the simplification is valid. $x = \dfrac{p^2 - 16}{p + 4}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = p$ $ b = \sqrt{16} = 4$ So we can rewrite the expression as: $x = \dfrac{({p} + {4})({p} {-4})} {p + 4} $ We can divide the numerator and denominator by $(p + 4)$ on condition that $p \neq -4$ Therefore $x = p - 4; p \neq -4$